。
She was named Mary.
Literal
[topic-は] Mary [quotative-と] was-named.
名付ける ('to name [someone/something]') is a transitive verb; here in the passive 名付けられた ('was named'). The と marks the name itself — quotative と marks not just speech but also the content of designations, namings, and definitions. メアリー is the standard katakana rendering of 'Mary' — Western names are universally written in katakana even when used as Japanese given names (which does happen, though rarely; some modern parents pick Western-influenced names). This sentence might describe a Japanese baby with a Western-style name, a foreign person named in Japanese narration, or a character in a translated work.